Answer:
The statements are not given, so i will answer it in the most general way possible:
First, let's recall two things:
Horizontal translation.
For a number A positive, we can move the graph of f(x) by A units to the right by the transformation g(x) = f(x - A)
Reflection over x
For a point (x, y), a reflection over the x-axis transforms this point into (x, - y).
Now let's analyze the problem:
A generic circle, of radius R and centered in the point (a, b) can be written as:
(x - a)^2 + (y - b)^2 = R^2.
Now let's translate this 4 units to the right:
(x - 4 - a)^2 + (y - b)^2 = R^2.
or in standard circle notation:
(x - (4 + a))^2 + (y - b)^2 = R^2.
Now the circle is centered in the point (a + 4, b).
Now let's do a reflection over the x-axis.
This means that the sign of y changes, so now we have:
(x - (4 + a))^2 + (-y - b)^2 = R^2.
But because the term with y is squared, this is the same than:
(x - (4 + a))^2 + (y + b)^2 = R^2.
Or, in standard circle notation:
(x - (4 + a))^2 + (y - (-b))^2 = R^2.
Then the circle is now centered in point (a + 4, -b).
So now you know where the circle is located, and also you can see that the radius of the circle never changed.
